glove-parity: functional relation carrier — out(rel) as a method (D-CMH-G1-4a)

[AdaWorldAPI]

What

A method Glove now carries functional relations. Each one declares:

• a key field on its own concept;
• the target concept's glove;
• where a call supplies the target's live plane and value lanes.

This is #1311's anchor rule, moved into the method layer. Relations that fan out are not covered here.

• out(rel) → Cond::Reaches → Filter::Semijoin(fk, target live plane). As in Gremlin, a traverser whose edge leads nowhere is dropped. A dangling key and a key pointing at a dead row both fail.
• out(rel).has(f, eq|neq) → Cond::Via → Filter::EqU32Via, negated for neq. The liveness test is emitted once per relation.
• count() after the hop counts anchor rows, because the anchor does not move.
• The following are refused by name:
  • a second hop (SecondHop)
  • values on the target (ValueThroughRelation)
  • dedup on the target (DedupThroughRelation)
  • where(method()) on the target (WhereThroughRelation)
  • in / both (FanOut)
• Target fields bind against the target's own basis, claims and binder. Errors name them as relation.field. The key itself joins required.
• A call names each target concept's population. A wrong or missing one is refused with CallError::ForeignUniverse.
• R2IL gap: the fold band has VIA but no GATHER. A relation method on R2IL returns CallError::FrontendGap { R2il, "GATHER" }. Methods without relations still run on both frontends.

There is no new op in Quack, mask-risc or R2IL. The Gremlin text form (decl.rs) loads out(rel) too.

Evidence

crates/lance-graph-glove-parity/tests/relation.rs has 7 tests. The fixture is a synthetic line -billed_to-> partner pair with dangling keys, dead partners and dead lines. Every answer is checked against a row loop over the field text at n ∈ {1, 64, 65, 4097}.

Six disable runs each turned red the test that names the guard:

guard removed	failing test
liveness test	row oracle + lowering
neq negation	row oracle
population check	the_target_population_is_checked_at_the_call
key in required	refusal + lowering
R2IL refusal	r2il_names_the_missing_gather
emit liveness once per relation	lowering

Removing the liveness test fails the oracle. So EqU32Via alone is not out(rel): it keeps rows whose target is dead.

Two existing refusal pins were updated because the behaviour changed:

• in/both now return FanOut.
• out(performed_by) on the SAP glove now composes, and preparation refuses it with UnknownRelation.

The crate suite passes, and clippy runs clean with -D warnings and fmt.

Board

• Plan gremlin-composable-algebra-v1.md §8 is new, and the matrix rows and counts are updated (DIRECT 10→12, COMPOSE 22→20).
• STATUS_BOARD.md is updated. G1-0..3 are marked Shipped (D-CMH-G1: Gremlin steps as composable ClassId methods — billable_hours calls is_billable, no new Rust #1508), and D-CMH-G1-4 is split into 4a (this PR) and the fan-out remainder.
• Added the entry 2026-10-12-functional-relation-carrier.md.

Still open

Fan-out (in, M:N, E(), outE/inV) and the second hop are still unsupported. D-SAG-1-4's multi-hop dependency is still blocked on the second hop.

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📒 Files selected for processing (19)

• .claude/board/STATUS_BOARD.md
• .claude/board/entries/2026-10-12-functional-relation-carrier.md
• .claude/board/entries/README.md
• .claude/plans/gremlin-composable-algebra-v1.md
• crates/lance-graph-glove-parity/examples/awareness_loop.rs
• crates/lance-graph-glove-parity/examples/compose_cost.rs
• crates/lance-graph-glove-parity/examples/method_cost.rs
• crates/lance-graph-glove-parity/examples/method_load.rs
• crates/lance-graph-glove-parity/src/awareness.rs
• crates/lance-graph-glove-parity/src/decl.rs
• crates/lance-graph-glove-parity/src/gremlin.rs
• crates/lance-graph-glove-parity/src/method.rs
• crates/lance-graph-glove-parity/tests/awareness.rs
• crates/lance-graph-glove-parity/tests/common/mod.rs
• crates/lance-graph-glove-parity/tests/declared.rs
• crates/lance-graph-glove-parity/tests/gremlin.rs
• crates/lance-graph-glove-parity/tests/method.rs
• crates/lance-graph-glove-parity/tests/polyfill.rs
• crates/lance-graph-glove-parity/tests/relation.rs

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